Algebra Problem: multiple variables?
For a wedding, Shered bought several dozen roses and several dozen carnations. The roses cost $15 per dozen, and the carnations cost $8 per dozen. Shered bought a total of 17 dozen flowers and paid a total of $192. How many roses did she buy?
Could you PLEASE explain step by step, I know this is basic algebra lol but I forgot..thanks (:
Comments
we have two equations: r = roses c= carnations
1) r + c = 17
2) 15r + 8c = 192
Use substitution: so take equation 1 subtract r from both sides and make it
c = 17 - r Now sub it into equation 2
15r + 8(17-r) = 192
15r + 136 - 8r = 192
7r + 136 = 192 subtract 136 from both sides
7r = 56 divide by 7
r = 8 now use r = 8 in equation 1
8 + c = 17
c = 9
so you will have 8 dozen roses and 9 dozen carnations
i am glade to help u
roses = x
carnations = y
You have two equations that "stem" (see what I did there?) from the information above. the first equation at the bottom of this paragraph correlates to the amount of money that Shered bought. She bought an X amount of roses at $15 a dozen, and a Y amount of carnations at $8 a dozen for a total of $192.
The second equation says that Shered bought an X amount of roses and a Y amount of carnations for a grand total of 17 dozens total.
1. 192 = 15x + 8y
2. 17 = x + y
17 - x = y <----- isolate your y-variable. Now that you have an equation that equals y, you can plug this into your first equation.
192 = 15x + 8(17 - x)
distribute.
192 = 15x + 136 - 8x
combine like terms
192 = 7x + 136
7x = 192 - 136
7x = 56
x = 8
Shered bought 8 dozen roses
Hope that helps!
r + c = 17
15 r + 8 c = 192
multiply eqn 1 by 8
8 r + 8 c = 136
subtract from eqn 2
7r = 56
r = 8
c = 9
No. Dozen Roses = r
No. Dozen Carnations = c
r + c = 17
c = 17 - r ............... Eq. 1
15r + 8c = 192 .... Eq. 2
Sub 17 - r from Eq. 1 for c in Eq. 2:
15r + 8(17 - r) = 192
15r + 136 - 8r = 192
7r = 192 - 136
7r = 56
r = 56 / 7
r = 8
Shered bought 8 doz. roses, or 96 roses.
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x + y = 17
15x + 8y = 192
- 8x - 8y = - 136
15x + 8y = 192
7x = 56
x = 8 and y = 9